The elastic moduli and mechanics of Populus tremuloides (Salicaceae) petioles in bending and torsion

Changes attending leaf development in the mechanical behavior and elastic moduli of the petioles of Populus tremuloides Michx. were examined in terms of total leaf weight (Wt), lamina and petiole weight (Wl and Wp), petiolar length (L), and lamina surface area (A). A primary concern was the extent to which two elastic moduli (Young's modulus E and the shear modulus G) of petioles changed over time and were correlated with one another. E and G were measured by means of multiple resonance frequency spectra, and together with the dimensions of cross sections through petioles, these two elastic moduli were used to estimate the stiffness of petioles in simple bending and torsion. Petiolar bending was predicted by means of a model incorporating expressions for both the bending stiffness (EI) and torsional rigidity (GJ), where I is the second moment of area and J is the torsional constant. The predictions from these models were compared to observed petiolar bendings due to Wl. Additionally, the frequency of the oscillatory motion of leaves (placed in a wind tunnel with a 1 m.sec-1 ambient wind speed, directed normal to the blade of the leaf) was determined. Results indicate that L, A, Wl, Wp, and Wt were positively correlated with the age of leaves (crudely estimated as a function of leaf plastochron index, LPI); these morphometric parameters were also correlated with the magnitudes of E and G. Also, G was positively and linearly correlated with E, and was, on the average, an order of magnitude less than E. EI and GJ were positively correlated with LPI. The relationships among E, G, EI, C and Wl, Wp, Wt are discussed in terms of leaf allometries.